The 21 cm multibeam receiver on the Parkes telescope has been used for many neutral hydrogen (HI) imaging projects, for example, the HI Parkes All Sky Survey (HIPASS) and the Southern Galactic Plane Survey. In many experiments to date, basic radio frequency interference (RFI) rejection has been accomplished on a per-feed basis, using the median statistic throughout the processing, which eliminates outliers in a nonparametric fashion at the expense of increased statistical noise. The classic 21 cm baseline ripple problem has been largely ignored, except for the subtraction of a coarse template which is calculated independently of feed, time, telescope elevation, and receiver rotation. The ripple is especially strong during the daytime, when the Sun acts as a broadband RFI noise source. Here we report on new techniques that we are developing, for application to raw, postcorrelation multibeam data, which handle RFI rejection and ripple suppression in more sophisticated ways. RFI can be identified by the presence of coincident outliers on multiple feeds, by sharp increases or decreases in flux time series that are inconsistent with a beam-smeared sky, and by the presence of highly polarized flux. We present our progress with this approach and highlight some remaining difficulties. We also present a novel technique for modeling the variation during telescope scans of 21 cm baseline ripple caused by stray continuum radiation undergoing multiple reflections in the telescope cavity and demonstrate its application to HIPASS data; this may increase the usefulness of daytime spectral line observing.